4 Search Results for "Diedrich, Florian"

Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.104
Improved Approximation Algorithms for Three-Dimensional Bin Packing

Authors: Debajyoti Kar, Arindam Khan, and Malin Rau

Published in: LIPIcs, Volume 334, 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)

Abstract
We study three fundamental three-dimensional (3D) geometric packing problems: 3D (Geometric) Bin Packing (3D-BP), 3D Strip Packing (3D-SP), and Minimum Volume Bounding Box (3D-MVBB), where given a set of 3D (rectangular) cuboids, the goal is to find an axis-aligned nonoverlapping packing of all cuboids. In 3D-BP, we need to pack the given cuboids into the minimum number of unit cube bins. In 3D-SP, we need to pack them into a 3D cuboid with a unit square base and minimum height. Finally, in 3D-MVBB, the goal is to pack into a cuboid box of minimum volume. It is NP-hard to even decide whether a set of rectangles can be packed into a unit square bin - giving an (absolute) approximation hardness of 2 for 3D-BP and 3D-SP. The previous best (absolute) approximation for all three problems is by Li and Cheng (SICOMP, 1990), who gave algorithms with approximation ratios of 13, 46/7, and 46/7+ε, respectively, for 3D-BP, 3D-SP, and 3D-MVBB. We provide improved approximation ratios of 6, 6, and 3+ε, respectively, for the three problems, for any constant ε > 0. For 3D-BP, in the asymptotic regime, Bansal, Correa, Kenyon, and Sviridenko (Math. Oper. Res., 2006) showed that there is no asymptotic polynomial-time approximation scheme (APTAS) even when all items have the same height. Caprara (Math. Oper. Res., 2008) gave an asymptotic approximation ratio of T_{∞}² + ε ≈ 2.86, where T_{∞} is the well-known Harmonic constant in Bin Packing. We provide an algorithm with an improved asymptotic approximation ratio of 3 T_{∞}/2 + ε ≈ 2.54. Further, we show that unlike 3D-BP (and 3D-SP), 3D-MVBB admits an APTAS.
Cite as

Debajyoti Kar, Arindam Khan, and Malin Rau. Improved Approximation Algorithms for Three-Dimensional Bin Packing. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 104:1-104:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{kar_et_al:LIPIcs.ICALP.2025.104,
  author =	{Kar, Debajyoti and Khan, Arindam and Rau, Malin},
  title =	{{Improved Approximation Algorithms for Three-Dimensional Bin Packing}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{104:1--104:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-372-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{334},
  editor =	{Censor-Hillel, Keren and Grandoni, Fabrizio and Ouaknine, Jo\"{e}l and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2025.104},
  URN =		{urn:nbn:de:0030-drops-234814},
  doi =		{10.4230/LIPIcs.ICALP.2025.104},
  annote =	{Keywords: Approximation Algorithms, Geometric Packing, Multidimensional Packing}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2025.60
Improved Approximation Algorithms for Three-Dimensional Knapsack

Authors: Klaus Jansen, Debajyoti Kar, Arindam Khan, K. V. N. Sreenivas, and Malte Tutas

Published in: LIPIcs, Volume 332, 41st International Symposium on Computational Geometry (SoCG 2025)

Abstract
We study the three-dimensional Knapsack (3DK) problem, in which we are given a set of axis-aligned cuboids with associated profits and an axis-aligned cube knapsack. The objective is to find a non-overlapping axis-aligned packing (by translation) of the maximum profit subset of cuboids into the cube. The previous best approximation algorithm is due to Diedrich, Harren, Jansen, Thöle, and Thomas (2008), who gave a (7+ε)-approximation algorithm for 3DK and a (5+ε)-approximation algorithm for the variant when the items can be rotated by 90 degrees around any axis, for any constant ε > 0. Chlebík and Chlebíková (2009) showed that the problem does not admit an asymptotic polynomial-time approximation scheme. We provide an improved polynomial-time (139/29+ε) ≈ 4.794-approximation algorithm for 3DK and (30/7+ε) ≈ 4.286-approximation when rotations by 90 degrees are allowed. We also provide improved approximation algorithms for several variants such as the cardinality case (when all items have the same profit) and uniform profit-density case (when the profit of an item is equal to its volume). Our key technical contribution is container packing - a structured packing in 3D such that all items are assigned into a constant number of containers, and each container is packed using a specific strategy based on its type. We first show the existence of highly profitable container packings. Thereafter, we show that one can find near-optimal container packing efficiently using a variant of the Generalized Assignment Problem (GAP).
Cite as

Klaus Jansen, Debajyoti Kar, Arindam Khan, K. V. N. Sreenivas, and Malte Tutas. Improved Approximation Algorithms for Three-Dimensional Knapsack. In 41st International Symposium on Computational Geometry (SoCG 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 332, pp. 60:1-60:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{jansen_et_al:LIPIcs.SoCG.2025.60,
  author =	{Jansen, Klaus and Kar, Debajyoti and Khan, Arindam and Sreenivas, K. V. N. and Tutas, Malte},
  title =	{{Improved Approximation Algorithms for Three-Dimensional Knapsack}},
  booktitle =	{41st International Symposium on Computational Geometry (SoCG 2025)},
  pages =	{60:1--60:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-370-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{332},
  editor =	{Aichholzer, Oswin and Wang, Haitao},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2025.60},
  URN =		{urn:nbn:de:0030-drops-232126},
  doi =		{10.4230/LIPIcs.SoCG.2025.60},
  annote =	{Keywords: Approximation Algorithms, Hyperrectangle Packing, Multidimensional Knapsack, Three-dimensional Packing}
}
Document
Extended Abstract
DOI: 10.4230/LIPIcs.TIME.2023.16
A Decomposition Framework for Inconsistency Handling in Qualitative Spatial and Temporal Reasoning (Extended Abstract)

Authors: Yakoub Salhi and Michael Sioutis

Published in: LIPIcs, Volume 278, 30th International Symposium on Temporal Representation and Reasoning (TIME 2023)

Abstract
Dealing with inconsistency is a central problem in AI, due to the fact that inconsistency can arise for many reasons in real-world applications, such as context dependency, multi-source information, vagueness, noisy data, etc. Among the approaches that are involved in inconsistency handling, we can mention argumentation, non-monotonic reasoning, and paraconsistency, e.g., see [Philippe Besnard and Anthony Hunter, 2008; Gerhard Brewka et al., 1997; Koji Tanaka et al., 2013]. In the work of [Yakoub Salhi and Michael Sioutis, 2023], we are interested in dealing with inconsistency in the context of Qualitative Spatio-Temporal Reasoning (QSTR) [Ligozat, 2013]. QSTR is an AI framework that aims to mimic, natural, human-like representation and reasoning regarding space and time. This framework is applied to a variety of domains, such as qualitative case-based reasoning and learning [Thiago Pedro Donadon Homem et al., 2020] and visual sensemaking [Jakob Suchan et al., 2021]; the interested reader is referred to [Michael Sioutis and Diedrich Wolter, 2021] for a recent survey. Motivation. In [Yakoub Salhi and Michael Sioutis, 2023], we study the decomposition of an inconsistent constraint network into consistent subnetworks under, possible, mandatory constraints. To illustrate the interest of such a decomposition, we provide a simple example described in Figure 1. The QCN depicted in the top part of the figure corresponds to a description of an inconsistent plan. Further, we assume that the constraint Task A {before} Task B is mandatory. To handle inconsistency, this plan can be transformed into a decomposition of two consistent plans, depicted in the bottom part of the figure; this decomposition can be used, e.g., to capture the fact that Task C must be performed twice. More generally, network decomposition can be involved in inconsistency handling in several ways: it can be used to identify potential contexts that explain the presence of inconsistent information; it can also be used to restore consistency through a compromise between the components of a decomposition, e.g., by using belief merging [Jean-François Condotta et al., 2010]; in addition, QCN decomposition can be used as the basis for defining inconsistency measures. Contributions. We summarize the contributions of [Yakoub Salhi and Michael Sioutis, 2023] as follows. First, we propose a theoretical study of a problem that consists in decomposing an inconsistent QCN into a bounded number of consistent QCNs that may satisfy a specified part in the original QCN; intuitively, the required common part corresponds to the constraints that are considered necessary, if any. To this end, we provide upper bounds for the minimum number of components in a decomposition as well as computational complexity results. Secondly, we provide two methods for solving our decomposition problem. The first method corresponds to a greedy constraint-based algorithm, a variant of which involves the use of spanning trees; the basic idea of this variant is that any acyclic constraint graph in QSTR is consistent, and such a graph can be used as a starting point for building consistent components. The second method corresponds to a SAT-based encoding; every model of this encoding is used to construct a valid decomposition. Thirdly, we consider two optimization versions of the initial decomposition problem that focus on minimizing the number of components and maximizing the similarity between components, respectively. The similarity between two QCNs is quantified by the number of common non-universal constraints; the interest in maximizing the similarity lies mainly in the fact that it reduces the number of constraints that allow each component to be distinguished from the rest. Of course, our previous methods are adapted to tackle these optimization versions, too. Additionally, we introduce two inconsistency measures based on QCN decomposition, which can be seen as counterparts of measures for propositional KBs introduced in [Matthias Thimm, 2016; Meriem Ammoura et al., 2017], and show that they satisfy several desired properties in the literature. Finally, we provide implementations of our methods for computing decompositions and experimentally evaluate them using different metrics.
Cite as

Yakoub Salhi and Michael Sioutis. A Decomposition Framework for Inconsistency Handling in Qualitative Spatial and Temporal Reasoning (Extended Abstract). In 30th International Symposium on Temporal Representation and Reasoning (TIME 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 278, pp. 16:1-16:3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{salhi_et_al:LIPIcs.TIME.2023.16,
  author =	{Salhi, Yakoub and Sioutis, Michael},
  title =	{{A Decomposition Framework for Inconsistency Handling in Qualitative Spatial and Temporal Reasoning}},
  booktitle =	{30th International Symposium on Temporal Representation and Reasoning (TIME 2023)},
  pages =	{16:1--16:3},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-298-3},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{278},
  editor =	{Artikis, Alexander and Bruse, Florian and Hunsberger, Luke},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TIME.2023.16},
  URN =		{urn:nbn:de:0030-drops-191062},
  doi =		{10.4230/LIPIcs.TIME.2023.16},
  annote =	{Keywords: Spatial and Temporal Reasoning, Qualitative Constraints, Inconsistency Handling, Decomposition, Inconsistency Measures}
}
Document
DOI: 10.4230/OASIcs.ATMOS.2015.42
Heuristic Approaches to Minimize Tour Duration for the TSP with Multiple Time Windows

Authors: Niklas Paulsen, Florian Diedrich, and Klaus Jansen

Published in: OASIcs, Volume 48, 15th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2015)

Abstract
We present heuristics to handle practical travelling salesman problems with multiple time windows per node, where the optimization goal is minimal tour duration, which is the time spent outside the depot node. We propose a dynamic programming approach which combines state labels by encoding intervals to handle the larger state space needed for this objective function. Our implementation is able to solve many practical instances in real-time and is used for heuristic search of near-optimal solutions for hard instances. In addition, we outline a hybrid genetic algorithm we implemented to cope with hard or unknown instances. Experimental evaluation proves the efficiency and suitability for practical use of our algorithms and even leads to improved upper bounds for yet unsolved instances from the literature.
Cite as

Niklas Paulsen, Florian Diedrich, and Klaus Jansen. Heuristic Approaches to Minimize Tour Duration for the TSP with Multiple Time Windows. In 15th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2015). Open Access Series in Informatics (OASIcs), Volume 48, pp. 42-55, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

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@InProceedings{paulsen_et_al:OASIcs.ATMOS.2015.42,
  author =	{Paulsen, Niklas and Diedrich, Florian and Jansen, Klaus},
  title =	{{Heuristic Approaches to Minimize Tour Duration for the TSP with Multiple Time Windows}},
  booktitle =	{15th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2015)},
  pages =	{42--55},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-939897-99-6},
  ISSN =	{2190-6807},
  year =	{2015},
  volume =	{48},
  editor =	{Italiano, Giuseppe F. and Schmidt, Marie},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2015.42},
  URN =		{urn:nbn:de:0030-drops-54608},
  doi =		{10.4230/OASIcs.ATMOS.2015.42},
  annote =	{Keywords: TSPTW, minimum tour duration, dynamic programming, heuristics}
}
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